Finite Group Databasebeta

← C3×#10596025 #13179306

Subgroups — C3×#10596025 #13179306

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C33×C4×D4C211yesmaximal, characteristic, complemented
4C3×#64139C212yesmaximal, complemented
5C2×C3×#3752C212yesmaximal, complemented
6C3×#64106C211yesmaximal, characteristic, complemented
7C3×#64104C211yesmaximal, characteristic, complemented
8C3×#64095C212yesmaximal, complemented
9C3×#64091C212yesmaximal, complemented
10C3×#64084C211yesmaximal, characteristic, complemented
11C3×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12#10596025C311yesmaximal, characteristic, direct product factor
13C3×#5554—34nomaximal
14C23×C3×C3⋊D3C2212yes—
15C2×C33×D4C2211yescharacteristic
16C22×C33×C4C2212yescomplemented
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yescomplemented
19C22×C3×C3⋊Dic3C2212yescomplemented
20C3×#3830—24no—
21C3×D4×C3⋊D3—24no—
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4⋊(C3⋊D3)C2212yescomplemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic
26C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
27C2×C3×#634C2211yescharacteristic, complemented
28C33×C4⋊C4C2211yescharacteristic, complemented
29C33×C22⋊C4C2212yescomplemented
30C33×C42C2211yescharacteristic, complemented
31C3×#3752C2211yescharacteristic
32C3×#3752C2212yes—
33C3×#3752C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C3×#3752C2212yescomplemented
36C3×#3752C2212yescomplemented
37C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
38C3×C4⋊(C3⋊Dic3)C2212yescomplemented
39C2×#3830C2×C311yescharacteristic, complemented
40C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
41C2×C3×#237—34no—
42C2×C3×D3×D4—34no—
43C32×C4×D4—24no—
44C32×C4×D4D314yescomplemented
45C32×C4×D4C2×C311yescharacteristic, complemented
46#64139C2×C312yescomplemented
47C2×#3752C2×C312yescomplemented
48#64106C2×C311yescharacteristic, complemented
49#64104C2×C311yescharacteristic, complemented
50#64095C2×C312yescomplemented
51#64091C2×C312yescomplemented
52#64084C2×C311yescharacteristic, complemented
53C4×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
54C3×#930—38no—
55C2×C3×(C2×D3)⋊C4—38no—
56C3×#897—34no—
57C3×#895—34no—
58C3×#886—38no—
59C3×#882—38no—
60C3×#875—34no—
61C3×C4×D12—34no—
62C23×C33C2312yes—
63C22×C3×C3⋊D3—24no—
64C22×C3×C3⋊D3—24no—
65C22×C3×C3⋊D3—42no—
66C22×C3×C3⋊D3C2312yes—
67C22×C3×C3⋊D3C2311yescharacteristic
68C22×C3×C3⋊D3C2311yescharacteristic
69C33×D4D414yescomplemented
70C2×C33×C4—42no—
71C2×C33×C4C2312yes—
72C2×C33×C4C2311yescharacteristic
73C2×C33×C4C2311yescharacteristic
74C2×C33×C4C2311yescharacteristic
75C3×#638—24no—
76C3×#638—24no—
77C2×C3×C3⋊Dic3—24no—
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2312yes—
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C3×C4⋊(C3⋊D3)—22no—
82C3×C4⋊(C3⋊D3)—22no—
83C3×C4⋊(C3⋊D3)—42no—
84C3×C4×C3⋊D3—22no—
85C3×C4×C3⋊D3—22no—
86C3×#634—22no—
87C3×#546—91no—
88#5554—34no—
89C23×C3⋊D3C22×C312yes—
90C23×C3×D3—38no—
91C2×C32×D4—24no—
92C2×C32×D4C2×D314yes—
93C2×C32×D4C22×C311yescharacteristic
94C22×C32×C4—28no—
95C22×C32×C4C2×D318yescomplemented
96C22×C32×C4C22×C312yescomplemented
97C2×#638C22×C312yes—
98C2×#638C22×C312yescomplemented
99C22×C3⋊Dic3C22×C312yescomplemented
100#3830—24no—
101D4×C3⋊D3—24no—
102C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
103C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
104C2×C4⋊(C3⋊D3)C22×C312yescomplemented
105C2×C4×C3⋊D3C22×C311yescharacteristic
106C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
107C2×#634C22×C311yescharacteristic, complemented
108C2×C3×#67—38no—
109C2×C3×#67—38no—
110C22×C3×Dic3—38no—
111C3×#237—616no—
112C3×D3×D4—616no—
113C2×C3×D12—34no—
114C2×C3×D12—34no—
115C2×C3×D12—38no—
116C2×C3×C4×D3—34no—
117C2×C3×C4×D3—34no—
118C2×C3×Dic6—34no—
119C32×C4⋊C4—24no—
120C32×C4⋊C4C2×D314yescomplemented
121C32×C4⋊C4C22×C311yescharacteristic, complemented
122C32×C22⋊C4—28no—
123C32×C22⋊C4C2×D318yescomplemented
124C32×C22⋊C4C22×C312yescomplemented
125C32×C42—24no—
126C32×C42C2×D314yescomplemented
127C32×C42C22×C311yescharacteristic, complemented
128#3752C22×C311yescharacteristic
129#3752C22×C312yes—
130#3752C22×C311yescharacteristic, complemented
131#3752C22×C312yescomplemented
132#3752C22×C312yescomplemented
133#3752C22×C312yescomplemented
134C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
135C4⋊(C3⋊Dic3)C22×C312yescomplemented
136C3×(C2×D3)⋊C4—38no—
137C3×(C2×D3)⋊C4—38no—
138C3×(C2×D3)⋊C4—38no—
139C3×(C2×D3)⋊C4—34no—
140C3×(C2×D3)⋊C4—38no—
141C3×(C2×D3)⋊C4—34no—
142C3×C4⋊Dic3—34no—
143C3×C4⋊Dic3—38no—
144C22×C33—22no—
145C22×C33—22no—
146C22×C33C2×D414yes—
147C22×C33C2411yescharacteristic
148C2×C3×C3⋊D3—21no—
149C2×C3×C3⋊D3—21no—
150C2×C3×C3⋊D3—21no—
151C2×C3×C3⋊D3—22no—
152C2×C3×C3⋊D3—21no—
153C2×C3×C3⋊D3—22no—
154C2×C3×C3⋊D3—21no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—48no—
157C2×C3×C3⋊D3#4112yescomplemented
158C33×C4—21no—
159C33×C4—21no—
160C33×C4—22no—
161C33×C4C2×D412yes—
162C3×C3⋊Dic3—22no—
163C3×C3⋊Dic3—21no—
164C3×C3⋊Dic3—21no—
165C2×C3×#41—91no—
166C22×C3×D4—91no—
167C2×#237—34no—
168C2×D3×D4—34no—
169C3×#124—91no—
170C3×#123—92no—
171C3×C22⋊Q8—91no—
172C3×#121—92no—
173C3×#121—91no—
174C3×#120—92no—
175C3×C4×D4—24no—
176C3×C4×D4—91no—
177C3×C4×D4C3×D314yescomplemented
178C3×C4×D4C3⋊D311yescharacteristic, complemented
179C2×C3×C22⋊C4—92no—
180#930—38no—
181C2×(C2×D3)⋊C4—38no—
182#897—34no—
183#895—34no—
184#886—38no—
185#882—38no—
186#875—34no—
187C4×D12—34no—
188C23×C32—28no—
189C23×C32C22×D318yes—
190C23×C32C23×C312yes—
191C22×C3⋊D3—24no—
192C22×C3⋊D3—24no—
193C22×C3⋊D3—42no—
194C22×C3⋊D3C23×C312yes—
195C22×C3⋊D3C23×C311yescharacteristic
196C22×C3⋊D3C23×C311yescharacteristic
197C22×C3×D3—34no—
198C22×C3×D3—38no—
199C22×C3×D3—34no—
200C22×C3×D3—616no—
201C22×C3×D3—616no—
202C22×C3×D3—128no—
203C32×D4—216no—
204C32×D4D12116yescomplemented
205C32×D4C3×D414yescomplemented
206C2×C32×C4—24no—
207C2×C32×C4—24no—
208C2×C32×C4—24no—
209C2×C32×C4—28no—
210C2×C32×C4—48no—
211C2×C32×C4—42no—
212C2×C32×C4—416no—
213C2×C32×C4C22×D314yes—
214C2×C32×C4C22×D318yes—
215C2×C32×C4C22×D314yes—
216C2×C32×C4C22×D314yes—
217C2×C32×C4C23×C312yes—
218C2×C32×C4C23×C311yescharacteristic
219C2×C32×C4C23×C311yescharacteristic
220C2×C32×C4C23×C311yescharacteristic
221#638—24no—
222#638—24no—
223C2×C3⋊Dic3—24no—
224C2×C3⋊Dic3C23×C311yescharacteristic
225C2×C3⋊Dic3C23×C312yes—
226C2×C3⋊Dic3C23×C311yescharacteristic
227C4⋊(C3⋊D3)—22no—
228C4⋊(C3⋊D3)—22no—
229C4⋊(C3⋊D3)—42no—
230C4×C3⋊D3—22no—
231C4×C3⋊D3—22no—
232#634—22no—
233C3×#67—616no—
234C3×#67—616no—
235C2×C3×Dic3—34no—
236C2×C3×Dic3—38no—
237C2×C3×Dic3—34no—
238C2×C3×Dic3—616no—
239C3×D12—68no—
240C3×D12—68no—
241C3×D12—128no—
242C3×C4×D3—68no—
243C3×C4×D3—68no—
244C3×Dic6—68no—
245#546—91noSylow
246C2×C33—24no—
247C2×C33C22×D411yescharacteristic
248C2×C33C2×#4111yescharacteristic
249C2×C33H(5,𝔽2)11yescharacteristic
250C3×C3⋊D3—22no—
251C3×C3⋊D3—41no—
252C3×C3⋊D3—42no—
253C24×C3—92no—
254C23×D3—38no—
255C3×#41—184no—
256C2×C3×Q8—91no—
257C2×C3×D4—24no—
258C2×C3×D4—92no—
259C2×C3×D4—92no—
260C2×C3×D4—91no—
261C2×C3×D4—91no—
262C2×C3×D4—92no—
263C2×C3×D4—184no—
264C2×C3×D4C2×C3×D314yes—
265C2×C3×D4C2×C3⋊D311yescharacteristic
266C22×C3×C4—28no—
267C22×C3×C4—92no—
268C22×C3×C4—91no—
269C22×C3×C4—91no—
270C22×C3×C4C2×C3×D318yescomplemented
271C22×C3×C4C2×C3⋊D312yescomplemented
272C2×#67—38no—
273C2×#67—38no—
274C22×Dic3—38no—
275#237—616no—
276D3×D4—616no—
277C2×D12—34no—
278C2×D12—34no—
279C2×D12—38no—
280C2×C4×D3—34no—
281C2×C4×D3—34no—
282C2×Dic6—34no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—91no—
285C3×C4⋊C4—92no—
286C3×C4⋊C4C2×C3×D314yescomplemented
287C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
288C3×C22⋊C4—28no—
289C3×C22⋊C4—91no—
290C3×C22⋊C4—92no—
291C3×C22⋊C4—92no—
292C3×C22⋊C4—92no—
293C3×C22⋊C4—91no—
294C3×C22⋊C4—92no—
295C3×C22⋊C4C2×C3×D318yescomplemented
296C3×C22⋊C4C2×C3⋊D312yescomplemented
297C3×C42—24no—
298C3×C42C2×C3×D314yescomplemented
299C3×C42C2×C3⋊D311yescharacteristic, complemented
300(C2×D3)⋊C4—34no—
301(C2×D3)⋊C4—34no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—38no—
304(C2×D3)⋊C4—38no—
305(C2×D3)⋊C4—38no—
306C4⋊Dic3—34no—
307C4⋊Dic3—38no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32—24no—
311C22×C32—216no—
312C22×C32—28no—
313C22×C32—28no—
314C22×C32—48no—
315C22×C32—48no—
316C22×C32C2×D12116yes—
317C22×C32C2×C3×D414yes—
318C22×C32C23×D314yes—
319C22×C32C24×C311yescharacteristic
320C2×C3⋊D3—21no—
321C2×C3⋊D3—21no—
322C2×C3⋊D3—21no—
323C2×C3⋊D3—22no—
324C2×C3⋊D3—21no—
325C2×C3⋊D3—22no—
326C2×C3⋊D3—21no—
327C2×C3⋊D3—22no—
328C2×C3⋊D3—48no—
329C2×C3⋊D3C3×#4112yescomplemented
330C2×C3×D3—38no—
331C2×C3×D3—64no—
332C2×C3×D3—64no—
333C2×C3×D3—64no—
334C2×C3×D3—68no—
335C2×C3×D3—64no—
336C2×C3×D3—68no—
337C2×C3×D3—64no—
338C2×C3×D3—68no—
339C2×C3×D3—1232no—
340C32×C4—28no—
341C32×C4—24no—
342C32×C4—21no—
343C32×C4—22no—
344C32×C4—21no—
345C32×C4—28no—
346C32×C4—28no—
347C32×C4—24no—
348C32×C4—44no—
349C32×C4—48no—
350C32×C4C2×D1218yes—
351C32×C4C2×C3×D412yes—
352C3⋊Dic3—22no—
353C3⋊Dic3—21no—
354C3⋊Dic3—21no—
355C3×Dic3—68no—
356C3×Dic3—64no—
357C3×Dic3—64no—
358C2×#41—91no—
359C22×D4—91no—
360#124—91no—
361#123—92no—
362C22⋊Q8—91no—
363#121—92no—
364#121—91no—
365#120—92no—
366C4×D4—91no—
367C4×D4C3×C3⋊D311yescharacteristic, complemented
368C2×C22⋊C4—92no—
369C33#54611yescharacteristic, complemented, Sylow
370C23×C3—28no—
371C23×C3—91no—
372C23×C3—92no—
373C23×C3—91no—
374C23×C3—184no—
375C23×C3—184no—
376C23×C3—362no—
377C23×C3C22×C3×D318yes—
378C23×C3C22×C3⋊D312yes—
379C22×D3—34no—
380C22×D3—38no—
381C22×D3—34no—
382C22×D3—616no—
383C22×D3—616no—
384C22×D3—128no—
385C3×Q8—182no—
386C3×D4—216no—
387C3×D4—182no—
388C3×D4—184no—
389C3×D4—184no—
390C3×D4—182no—
391C3×D4—362no—
392C3×D4C3×D12116yescomplemented
393C3×D4C4⋊(C3⋊D3)14yescomplemented
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—28no—
398C2×C3×C4—48no—
399C2×C3×C4—42no—
400C2×C3×C4—416no—
401C2×C3×C4—91no—
402C2×C3×C4—92no—
403C2×C3×C4—91no—
404C2×C3×C4—184no—
405C2×C3×C4—182no—
406C2×C3×C4—182no—
407C2×C3×C4C22×C3×D314yes—
408C2×C3×C4C22×C3×D318yes—
409C2×C3×C4C22×C3×D314yes—
410C2×C3×C4C22×C3×D314yes—
411C2×C3×C4C22×C3⋊D311yescharacteristic
412C2×C3×C4C22×C3⋊D311yescharacteristic
413C2×C3×C4C22×C3⋊D312yes—
414C2×C3×C4C22×C3⋊D311yescharacteristic
415#67—616no—
416#67—616no—
417C2×Dic3—34no—
418C2×Dic3—38no—
419C2×Dic3—34no—
420C2×Dic3—616no—
421D12—68no—
422D12—68no—
423D12—128no—
424C4×D3—68no—
425C4×D3—68no—
426Dic6—68no—
427C2×C32—24no—
428C2×C32—24no—
429C2×C32—24no—
430C2×C32—24no—
431C2×C32—216no—
432C2×C32—416no—
433C2×C32C22×D1214yes—
434C2×C32#100414yes—
435C2×C32D3×#4114yes—
436C2×C32C22×C3×D411yescharacteristic
437C2×C32C2×C3×#4111yescharacteristic
438C2×C32C3×H(5,𝔽2)11yescharacteristic
439C3⋊D3—22no—
440C3⋊D3—41no—
441C3⋊D3—42no—
442C3×D3—68no—
443C3×D3—124no—
444C3×D3—128no—
445C24—92no—
446#41—184no—
447C2×Q8—91no—
448C2×D4—92no—
449C2×D4—92no—
450C2×D4—91no—
451C2×D4—91no—
452C2×D4—92no—
453C2×D4—184no—
454C2×D4C2×C3×C3⋊D311yescharacteristic
455C22×C4—92no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4C2×C3×C3⋊D312yescomplemented
459C4⋊C4—91no—
460C4⋊C4—92no—
461C4⋊C4C2×C3×C3⋊D311yescharacteristic, complemented
462C22⋊C4—91no—
463C22⋊C4—92no—
464C22⋊C4—92no—
465C22⋊C4—92no—
466C22⋊C4—91no—
467C22⋊C4—92no—
468C22⋊C4C2×C3×C3⋊D312yescomplemented
469C42C2×C3×C3⋊D311yescharacteristic, complemented
470C22×C3—28no—
471C22×C3—28no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—216no—
476C22×C3—48no—
477C22×C3—48no—
478C22×C3—92no—
479C22×C3—181no—
480C22×C3—181no—
481C22×C3—181no—
482C22×C3—182no—
483C22×C3—181no—
484C22×C3—182no—
485C22×C3—181no—
486C22×C3—182no—
487C22×C3—368no—
488C22×C3C2×C3×D12116yes—
489C22×C3C2×C4⋊(C3⋊D3)14yes—
490C22×C3C23×C3×D314yes—
491C22×C3C23×C3⋊D311yescharacteristic
492C2×D3—38no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—64no—
496C2×D3—68no—
497C2×D3—64no—
498C2×D3—68no—
499C2×D3—64no—
500C2×D3—68no—
501C2×D3—1232no—
502C3×C4—28no—
503C3×C4—28no—
504C3×C4—24no—
505C3×C4—24no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—21no—
509C3×C4—28no—
510C3×C4—48no—
511C3×C4—44no—
512C3×C4—181no—
513C3×C4—181no—
514C3×C4—182no—
515C3×C4C2×C3×D1218yes—
516C3×C4C2×C4⋊(C3⋊D3)12yes—
517Dic3—68no—
518Dic3—64no—
519Dic3—64no—
520C32—24no—
521C32#555414yescomplemented
522C32C3×#54611yescharacteristic, complemented
523C23—91no—
524C23—92no—
525C23—91no—
526C23—184no—
527C23—184no—
528C23—362no—
529C23C22×C3×C3⋊D312yes—
530Q8—182no—
531D4—182no—
532D4—184no—
533D4—184no—
534D4—182no—
535D4—362no—
536D4C3×C4⋊(C3⋊D3)14yescomplemented
537C2×C4—42no—
538C2×C4—91no—
539C2×C4—92no—
540C2×C4—91no—
541C2×C4—184no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4C22×C3×C3⋊D311yescharacteristic
545C2×C4C22×C3×C3⋊D311yescharacteristic
546C2×C4C22×C3×C3⋊D312yes—
547C2×C4C22×C3×C3⋊D311yescharacteristic
548C2×C3—216no—
549C2×C3—24no—
550C2×C3—24no—
551C2×C3—24no—
552C2×C3—24no—
553C2×C3—416no—
554C2×C3—182no—
555C2×C3—362no—
556C2×C3—361no—
557C2×C3C22×C3×D1214yes—
558C2×C3C3×#100414yes—
559C2×C3C3×D3×#4114yes—
560C2×C3C22×C4⋊(C3⋊D3)11yescharacteristic
561C2×C3#6436111yescharacteristic
562C2×C3#41×C3⋊D311yescharacteristic
563D3—68no—
564D3—128no—
565D3—124no—
566C22—22no—
567C22—22no—
568C22—92no—
569C22—181no—
570C22—181no—
571C22—181no—
572C22—182no—
573C22—181no—
574C22—182no—
575C22—181no—
576C22—182no—
577C22—368no—
578C22C2×C3×C4⋊(C3⋊D3)14yes—
579C22C23×C3×C3⋊D311yescharacteristic
580C4—21no—
581C4—22no—
582C4—21no—
583C4—181no—
584C4—181no—
585C4—182no—
586C4C2×C3×C4⋊(C3⋊D3)12yes—
587C3—24no—
588C3C3×#555414yescomplemented
589C3#1059602511yescharacteristic, direct product factor
590C2—24no—
591C2—182no—
592C2—362no—
593C2—361no—
594C2C22×C3×C4⋊(C3⋊D3)11yescharacteristic
595C2C3×#6436111yescharacteristic
596C2C3×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC22×C3C23×C3⋊D3
commutator, cosocleC22×C32C24×C3
FrattiniC22C23×C3×C3⋊D3
FittingC33×C4×D4C2
socleC22×C33C24
hypercenterC3×C4×D4C3⋊D3
hypocenterC32C3×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C33×C4×D4C2semidirect
4. C3×#64139C2semidirect
5. C2×C3×#3752C2semidirect
6. C3×#64106C2semidirect
7. C3×#64104C2semidirect
8. C3×#64095C2semidirect
9. C3×#64091C2semidirect
10. C3×#64084C2semidirect
11. C3×C4×C4⋊(C3⋊D3)C2semidirect
12. #10596025C3direct (N × H)
16. C22×C33×C4C22semidirect
18. C2×C3×#638C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×C4×C3⋊D3C22semidirect
27. C2×C3×#634C22semidirect
28. C33×C4⋊C4C22semidirect
29. C33×C22⋊C4C22semidirect
30. C33×C42C22semidirect
33. C3×#3752C22semidirect
34. C3×#3752C22semidirect
35. C3×#3752C22semidirect
36. C3×#3752C22semidirect
37. C3×C4⋊(C3⋊Dic3)C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C2×#3830C2×C3semidirect
40. C2×D4×C3⋊D3C2×C3semidirect
44. C32×C4×D4D3semidirect
45. C32×C4×D4C2×C3semidirect
46. #64139C2×C3semidirect
47. C2×#3752C2×C3semidirect
48. #64106C2×C3semidirect
49. #64104C2×C3semidirect
50. #64095C2×C3semidirect
51. #64091C2×C3semidirect
52. #64084C2×C3semidirect
53. C4×C4⋊(C3⋊D3)C2×C3semidirect
69. C33×D4D4semidirect
95. C22×C32×C4C2×D3semidirect
96. C22×C32×C4C22×C3semidirect
98. C2×#638C22×C3semidirect
99. C22×C3⋊Dic3C22×C3semidirect
104. C2×C4⋊(C3⋊D3)C22×C3semidirect
106. C2×C4×C3⋊D3C22×C3semidirect
107. C2×#634C22×C3semidirect
120. C32×C4⋊C4C2×D3semidirect
121. C32×C4⋊C4C22×C3semidirect
123. C32×C22⋊C4C2×D3semidirect
124. C32×C22⋊C4C22×C3semidirect
126. C32×C42C2×D3semidirect
127. C32×C42C22×C3semidirect
130. #3752C22×C3semidirect
131. #3752C22×C3semidirect
132. #3752C22×C3semidirect
133. #3752C22×C3semidirect
134. C4⋊(C3⋊Dic3)C22×C3semidirect
135. C4⋊(C3⋊Dic3)C22×C3semidirect
157. C2×C3×C3⋊D3#41semidirect
177. C3×C4×D4C3×D3semidirect
178. C3×C4×D4C3⋊D3semidirect
204. C32×D4D12semidirect
205. C32×D4C3×D4semidirect
270. C22×C3×C4C2×C3×D3semidirect
271. C22×C3×C4C2×C3⋊D3semidirect
286. C3×C4⋊C4C2×C3×D3semidirect
287. C3×C4⋊C4C2×C3⋊D3semidirect
295. C3×C22⋊C4C2×C3×D3semidirect
296. C3×C22⋊C4C2×C3⋊D3semidirect
298. C3×C42C2×C3×D3semidirect
299. C3×C42C2×C3⋊D3semidirect
329. C2×C3⋊D3C3×#41semidirect
367. C4×D4C3×C3⋊D3semidirect
369. C33#546semidirect
392. C3×D4C3×D12semidirect
393. C3×D4C4⋊(C3⋊D3)semidirect
458. C22×C4C2×C3×C3⋊D3semidirect
461. C4⋊C4C2×C3×C3⋊D3semidirect
468. C22⋊C4C2×C3×C3⋊D3semidirect
469. C42C2×C3×C3⋊D3semidirect
521. C32#5554semidirect
522. C32C3×#546semidirect
536. D4C3×C4⋊(C3⋊D3)semidirect
588. C3C3×#5554semidirect
589. C3#10596025direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#38302
C2×C3×D4×C3⋊D32
C33×C4×D42
C3×#641392
C2×C3×#37522
C3×#641062
C3×#641042
C3×#640952
C3×#640912
C3×#640842
C3×C4×C4⋊(C3⋊D3)2
#105960253
C3×#55543